WASHINGTON — The American Medical Association has long battled Democrats who oppose protecting doctors from malpractice lawsuits. But during a private meeting at the White House last month, association officials said, they found one Democrat willing to entertain the idea: President Obama.

In closed-door talks, Mr. Obama has been making the case that reducing malpractice lawsuits — a goal of many doctors and Republicans — can help drive down health care costs, and should be considered as part of any health care overhaul, according to lawmakers of both parties, as well as A.M.A. officials.

It is a position that could hurt Mr. Obama with the left wing of his party and with trial lawyers who are major donors to Democratic campaigns. But one Democrat close to the president said Mr. Obama, who wants health legislation to have broad support, views addressing medical liability issues as a “credibility builder” — in effect, a bargaining chip that might keep doctors and, more important, Republicans, at the negotiating table.

On Monday, Mr. Obama will go to the annual medical association meeting to face a group that has come out against a central component of his broader health care proposal — his call for a new public insurance program that would compete with the private plans. The White House says he will make the case that “reform is the single most important thing we can do for America’s long-term fiscal health,” and how important it is to have the cooperation of doctors.

But whether he can get them on board is an open question. The speech comes as the president’s ideas on health reform are facing mounting criticism — not only from the A.M.A. and Republicans, who also vehemently oppose a new public plan, but also from the hospital industry, which is up in arms over a proposal Mr. Obama announced on Saturday to pay for his health care overhaul in part by cutting certain hospital reimbursements.

Medical liability is an important component of the debate, but that, too, is controversial. White House officials said Mr. Obama was likely to refer to the issue in his speech to the medical association, but would not offer any specific proposal.

Mr. Obama has not endorsed capping malpractice jury awards, as did his predecessor, President George W. Bush. But as a senator, he advanced legislation aimed at reducing malpractice suits. And Dr. J. James Rohack, the incoming president of the medical association, said Mr. Obama told him at a meeting last month that he was open to offering some liability protection to doctors who follow standard guidelines for medical practice.

“If everyone is focused on saying, ‘How do we get rid of unnecessary costs,’ ” Dr. Rohack said, recounting the conversation, “if we as physicians are going to say, ‘Here’s our guidelines, we will follow them,’ then we need to have some protections. He listened and he said, ‘Clearly, that concept is worthy of discussion.’ ”

Health care experts estimate that preventable medical errors kill more than 100,000 Americans each year, yet doctors and hospitals, fearing lawsuits, do not openly discuss their mistakes — an impediment to improving quality of care. At the same time, doctors complain that “defensive medicine” — ordering tests and procedures out of fear of being sued — drives up health costs.

On Capitol Hill, Democrats drafting health legislation have so far shown little appetite for tackling the liability issue. But one Republican who met with Mr. Obama in April recalled that the president said he was willing to go against his party to get medical malpractice reforms into a health bill — but that he would expect Republican support for the legislation if he did so.

Mr. Obama also raised the issue at a recent meeting with two dozen Senate Democrats, some who attended said.

“He’s touched on this issue at a number of meetings,” said Senator Ron Wyden, Democrat of Oregon, who is also a proponent of liability reform. Mr. Wyden said the president articulated “the common sense message that if doctors act in line with their own professional guidelines, that ought to create a certain presumption that they have acted reasonably.”

As a senator, Mr. Obama joined Senator Hillary Rodham Clinton in 2005 in proposing legislation aimed at reducing both medical errors and lawsuits through a program known as Sorry Works, rooted in the idea that injured patients value an apology as much as money. Their bill encouraged doctors and hospitals to investigate errors and apologize for mistakes, to facilitate what Mr. Obama described as “a reasonable settlement that keeps the case out of court.”

Although the A.M.A.’s highest legislative priority is capping jury awards, highly unlikely under the Obama administration, it does favor legislation like that proposed by Senators Obama and Clinton. Dr. Rohack said the group’s legislative experts were also working over the weekend to draft a bill that would set out a way to protect doctors who are sued if they have followed professional practice guidelines.

“We are supportive of anything that may reduce liability,” Dr. Rohack said, adding that he was heartened by Mr. Obama’s “recognition that defensive medicine contributes to unnecessary health costs.”

But to deliver a deal with doctors, Mr. Obama would probably have to defy senior members of his party in both houses of Congress. Many Democrats oppose putting limits on medical lawsuits because they believe it is ineffective and unfair to patients.

Senator Max Baucus of Montana, the chairman of the Senate Finance Committee, is expected to outline his proposal for a health care overhaul this week, and aides said liability protection for doctors is not part of the plan.

Senator Harry Reid of Nevada, the Democratic leader, resisted medical malpractice legislation when it was pushed by Republicans in the past. “The whole premise of a medical malpractice ‘crisis’ is unfounded,” Mr. Reid said on the Senate floor in 2006, in a speech that quoted extensively from a book titled “The Medical Malpractice Myth.”

And any effort to restrict patients’ legal rights to sue will face tough opposition from the American Association for Justice, which represents trial lawyers and has met with Nancy-Ann DeParle, Mr. Obama’s point person for health reform, to express its concerns. Linda Lipsen, the association’s chief lobbyist, said practice guidelines were established by unregulated medical societies and “should not be conclusive” in a court of law.

The association may have an ally in Mr. Obama’s health secretary, Kathleen Sebelius, who is a former director of the Kansas Trial Lawyers Association. But Mr. Obama’s first choice for health secretary, Tom Daschle, who advised the president throughout the campaign, was a strong proponent of linking evidence-based medicine with protections against lawsuits.

And another top health adviser to Mr. Obama, Dr. Ezekiel J. Emanuel, has written extensively on liability reform.

“There is no doubt that comprehensive health care reform requires a monumental change to the current malpractice system, which not only hurts both doctors and patients, but also is far too expensive,” Dr. Emanuel, the brother of the White House chief of staff, Rahm Emanuel, wrote in a 2008 book, “Healthcare Guaranteed: A Simple, Secure Solution for America.”

But Mr. Obama has signaled that the solution may not be all that simple. Speaking to a group of chief executives in March, Mr. Obama said malpractice law changes should be part of the health care debate, although he conceded it would not be an easy sell.

“Medical liability issues — I think all those things have to be on the table,” Mr. Obama said. “And I won’t lie to you that everybody agrees on this theoretically until you start getting into the specifics.”